This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 11-042733, filed Feb. 22, 1999, the entire contents of which are incorporated herein by reference.
The present invention relates to a method of simulating an optical image, using an exposure mask. Particularly, the invention relates to a method of increasing the accuracy of predicting the simulated shapes of the corners of a mask pattern.
Patterns to be transferred to a semiconductor wafer to manufacture LSIs have become more microminiature. To transfer microminiature patterns to a semiconductor wafer, various techniques are now employed. Among these are: using, in the exposure apparatus, a light source that emit light of a short wavelength; utilizing a projection optical system that has an increased numerical aperture; using high-resolution resists; applying super resolution techniques (using modified illumination) phase-shifted masks.
Thanks to these techniques, it has become possible to transfer patterns having small k1 values. (A k1 value is a pattern size normalized with xcex/NA, where is the wavelength of the light applied in the exposure apparatus and NA is the numerical aperture of projection optical system.) When a low-k1 pattern is transferred to a wafer, its shape deviates from the desired shape due to optical proximity effect.
In order to correct the shape of the pattern from deviating from the desired one, a resist pattern based on the design pattern is simulated. The design pattern is modified in accordance with the results of simulation, so that the pattern transferred to the wafer may be identical in shape to the desired pattern.
Most methods of simulating a resist pattern obtained from the design pattern of an exposure mask, which is shaped like the design, are to perform various calculations based on Fourier imaging theory. In recent years, patterns have become more microminiature, and the transfer magnification has been changed from ⅕ to xc2xc, the elements of the pattern on the mask now have a width of less than 1 xcexcm. The pattern formed on the exposure mask conspicuously deviates in shape from the desired pattern.
The pattern on the exposure mask deviates in shape from the desired pattern, particularly at its corners. More precisely, the corners are rounded though they should be angled, causing so-called xe2x80x9ccorner rounding.xe2x80x9d If light is applied to a resist through the exposure mask having this undesired pattern, a significant difference in shape will occur between the resultant resist pattern and a resist pattern simulated directly based on the design pattern.
Two main factors determine the degree of corner rounding in the exposure mask pattern. The first factor is the resolution of the mask-drawing apparatus used. The second factor is the etching process performed.
The resolution of the mask-drawing apparatus depends on the diameter of the mask-drawing beam applied. It is generally expected that the resolution of the mask-drawing apparatus will not cause an outside corner and an inside corner of a mask pattern element to have different shapes. Hence, the first factor of determining the degree of corner rounding can hardly be said to result in a difference between the outside and inside corners the mask pattern element in terms of rounding.
In many cases, however, a mask pattern is etched a little more than the resist pattern size for enhancing the uniformity in planar mask size. Consequently, an outside corner and an inside corner of a mask pattern element will have difference shapes due to the second factor determining the degree of corner rounding.
With reference to FIG. 9, it will be described how the outside corner and inside corner of a mask pattern element are rounded to different degrees. Assume that a resist pattern 71 has been formed by a mask-drawing process. The hatching indicates the area on which the resist remains. After the resist pattern 71 is developed, its corners are rounded, each having the same radius (R) of curvature. This pattern 71 may be used as an etching mask to process a mask shield (made of Cr or the like). In this case, the pattern 71 is etched a little more than necessary, by an over-etching distance of xcex94x.
Assume that the etching proceeds along a normal to the surface being etched. Then, it is expected that the resist pattern will have a shape 72. Any outside corner of the pattern will have a smaller radius of curvature, Rxe2x88x92xcex94x, whereas the any inside corner will have a larger radius of curvature, R+xcex94x. Obviously, the outside and inside corners of the resist pattern have been rounded to different degrees.
The object of the present invention is to provide a method of processing exposure-mask pattern data, thereby to render a pattern used in simulation similar to a pattern actually used, in order to increase the precision of simulation. Another object of the invention is to provide a method of performing simulation. Still another object of the invention is to provide a recording medium.
According to the present invention, there is provided a method of processing exposure mask-pattern data. The method comprises the steps of: performing a re-sizing process of adding a prescribed positive bias xcex94 to design data of an exposure mask pattern (which is defined as opaque are on the mask), thereby forming first mask-pattern data; performing a corner process on each corner represented by the first mask-pattern data, thereby forming second mask-pattern data; and performing a re-sizing process of adding a prescribed negative bias xcex94xe2x80x2 to the second mask-pattern data, thereby forming third mask-pattern data.
According to the invention, there is provided a method of simulating an optical image by applying light through an exposure mask pattern. This method comprises the steps of: performing a re-sizing process of adding a prescribed positive bias xcex94 to design data of the exposure mask pattern, thereby forming first mask-pattern data; performing a corner process on each corner represented by the first mask-pattern data, thereby forming second mask-pattern data; performing a re-sizing process of adding a prescribed negative bias xcex94xe2x80x2 to the second mask-pattern data, thereby forming third mask-pattern data; setting exposure conditions; and calculating a optical image in accordance with the third mask pattern data and the exposure conditions, on a substrate to which light is applied through the exposure mask pattern.
According to the present invention, there is provided a recording medium, which stores a program for causing a computer to process the exposure mask-pattern data.
In the method of processing exposure-mask pattern data, the method of simulating an optical image, and the recording medium, all described above, it is desired that:
(a) The sum of the positive bias xcex94 and negative bias xcex94xe2x80x2 should be a mask bias for the design data of the exposure mask pattern, and the positive bias xcex94 corresponds to a bias for a mask-drawing resist pattern.
(b) The corner process should be to round each corner represented by the first mask-pattern data, thereby forming an arc which has a radius R and which inscribes the corner.
(c) The corner process should be to replace, at each corner represented by the first mask-pattern data, an arc having a radius R and inscribing the corner, by a plurality of continuous lines.
(d) A change in area of a pattern, which takes place after the arc has been replaced by a plurality of continuous lines, should be equal to a change in area of the pattern, which occurs when the corner is changed to an arc having a radius R and inscribing the corner.
Thanks to the characterizing features described above, the present invention is advantageous in the following respects.
The mask formed by the method according to the invention has a shape similar to the shape of the mask pattern that is formed in practice. Hence, when the exposure mask-pattern data is processed by the method described above, it is possible to calculate a high-precision optical image. In addition, the load on data processing does not increase so much as in the method wherein a uniform corner process is performed on mask pattern data.
Additional objects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out hereinafter.